{
  "id": "1610.00423",
  "version": "v1",
  "published": "2016-10-03T06:45:10.000Z",
  "updated": "2016-10-03T06:45:10.000Z",
  "title": "Decomposition of functions between Banach spaces in the orthogonality equation",
  "authors": [
    "Maysam Maysami Sadr"
  ],
  "comment": "Keywords: orthogonality equation; Banach space; bounded linear operator",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $E,F$ be Banach spaces. In the case that $F$ is reflexive we give a description for the solutions $(f,g)$ of the Banach-orthogonality equation $$\\langle f(x),g(\\alpha)\\rangle=\\langle x,\\alpha\\rangle\\hspace{10mm}\\forall x\\in E,\\forall \\alpha\\in E^*,$$ where $f:E\\rightarrow F,g:E^*\\rightarrow F^*$ are two maps. Our result generalizes the recent result of {\\L}ukasik and W\\'{o}jcik in the case that $E$ and $F$ are Hilbert spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-03T06:45:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B52",
      "47A05",
      "47A62"
    ],
    "keywords": [
      "banach spaces",
      "decomposition",
      "hilbert spaces",
      "result generalizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}